Question

Suppose that two competing firms, \(A\) and \(B\), produce a homogeneous good. Both firms have a marginal cost of \(\mathrm{MC}=\$ 50 .\) Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium, and (iii) Bertrand equilibrium. a. Because Firm \(A\) must increase wages, its \(\mathrm{MC}\) increases to \(\$ 80\). b. The marginal cost of both firms increases. c. The demand curve shifts to the right.

Short answer

The central idea is that the behavior of firms and hence the outcome depends substantially on the type of competition. Different market scenarios will produce different results in Cournot, collusive, and Bertrand equilibriums.

Step-by-step solution

Understanding the equilibriums

The Cournot equilibrium is characterized by firms choosing their quantity of production jointly, acknowledging that their decision affects the market price. In a collusive equilibrium, firms cooperate to maximize their joint profit, often by agreeing to produce a certain quantity or price. The Bertrand equilibrium involves firms choosing prices independently, anticipating that their competitors' prices will remain constant.

Situation (a) Increase in MC of Firm A

(i) In a Cournot equilibrium, as Firm A's marginal cost increases, it will reduce its quantity of production which will increase the market price. Firm B will seize the opportunity by producing more and increasing its profit. (ii) In a collusive equilibrium, the firms may choose to raise the market price to make up for Firm A's increased cost of production. (iii) In a Bertrand equilibrium, as firm A raises its price due to higher cost, firm B will not change its price and will capture the entire market.

Situation (b) MC of both firms increases

(i) In a Cournot equilibrium, both firms will reduce their quantity of production, leading to higher market prices. (ii) In a collusive equilibrium, both firms may agree to raise prices to absorb the increased cost. (iii) In a Bertrand equilibrium, as both firms face higher costs, they are likely to pass it onto consumers by raising their prices.

Situation (c) Demand curve shifts right

(i) In a Cournot equilibrium, the rise in demand leads to a larger market size that both firms could exploit. Both firms would increase their quantities resulting in a higher price as long as the marginal cost remains constant. (ii) In a collusive equilibrium, the firms might decide to keep production constant and increase the price. (iii) In a Bertrand equilibrium, as demand increases, both firms would increase their quantities to meet the larger market, leading to higher prices only if the increased demand is price inelastic.

Key concepts

Cournot Equilibrium

In a Cournot equilibrium, firms simultaneously choose how much to produce, under the assumption that their competitors will hold their output constant. This creates a strategic interdependence as each firm's decision influences the market price and their rival's profits. Imagine two runners on parallel tracks; they're not running together but certainly affect each other's pace. In the context of rising marginal costs for one firm, say Firm A, the firm would cut back on its production to maintain profitability. This would give an incentive to Firm B to expand its output to fill the gap left by Firm A, leading to a new equilibrium.

However, if the industry as a whole faces increased marginal costs, both firms would reduce their quantity, effectively driving the price up for consumers. This delicate balance of actions and reactions underscores the complexity within an oligopolistic market structure and highlights the critical role marginal cost plays in determining a firm's quantity of output.

Collusive Equilibrium

Imagine two friends in a schoolyard sharing a secret plan; that's somewhat like a collusive equilibrium, where firms act together rather than independently, essentially setting market conditions that favor them. They could determine a fixed price, decide on the quantity of production, or divide the market among themselves to maximize their combined profits while disregarding consumer welfare or competitive pressures.

In the face of rising costs for one or both firms, a collusive agreement might lead to a new higher price. This is done to shield the firms' profits from the increased expenses. While such behavior often violates competition laws, it illustrates the inherent tension between industry collaboration and market competition.

Bertrand Equilibrium

Unlike the Cournot equilibrium which focuses on quantities, the Bertrand equilibrium centers on price competition. Two ice cream stands on a beach setting prices independently would understand this well. Even a small price difference could lead customers to choose the cheaper option, forcing the competitors to consider their pricing meticulously. In a scenario where one firm's marginal cost increases, such as Firm A, it would have to raise its prices. Meanwhile, Firm B could maintain its price and attract customers away from Firm A, potentially monopolizing the market. Alternatively, if both firms faced increased costs, they might both increase their prices. In an ideal Bertrand scenario, however, prices tend to gravitate towards marginal costs over time, ensuring minimum profit margins.

Marginal Cost

Marginal cost is the cost of producing one additional unit of goods. It is a fundamental concept in economics, serving as a guidepost for a firm when it comes to making decisions on production levels. If we think of baking cookies, the marginal cost would include the materials and labor for that one extra cookie. A firm's marginal cost impacts its behavior in competitive settings; higher marginal costs might limit production, while lower marginal costs can encourage expansion. Firm A, facing wage hikes, must grapple with these decisions if their marginal cost goes up. In an oligopolistic market, such cost changes can ripple through to affect overall supply, demand, and market price dynamics.

Market Price

Market price is the current price at which an asset or service can be bought or sold. It's the meeting point of buyers' willingness to pay and sellers' willingness to accept, akin to haggling at a flea market until both parties nod in agreement. In an oligopoly, market price is heavily influenced by firm behavior – whether competitive like in the Bertrand model, cooperative as in collusive arrangements, or somewhere in between like Cournot competitors. Market prices fluctuate based on demand and supply changes, influenced by factors such as a firm’s rising marginal cost or a rightward shift in the demand curve. The dance of supply and demand in setting the market price keeps the market dynamic and sometimes unpredictable, reflecting the ever-changing nature of our economy.